To simplify the following discussion, the present invention will first be explained in terms of a frequency standard.
One class of frequency standards utilizes Coherent-Population-Trapping (CPT) in quantum absorbers. CPT-based frequency standards are described in U.S. Pat. Nos. 6,363,091 and 6,201,821, which are hereby incorporated by reference. Since such frequency standards are known to the art, they will not be described in detail here. For the purposes of the present discussion, it is sufficient to note that in such standards, the output of an electromagnetic source that has two frequency components with respective frequencies νL+½μ and νL−½μ (CPT-generating frequency components), and possibly other additional components, is applied to a quantum absorber. Here, νL is the average frequency of the CPT-generating components. The average vacuum wavelength of the electromagnetic source is approximately c/νL, where c is the speed of light in a vacuum. The quantum absorber has two low energy states (which shall be referred to as state A and state B), and n high energy states, each of which can be reached by a transition from state A and by a transition from state B. Denote the high energy states by Ck, for 1≦k≦n. Additionally, the quantum absorber may have any number of other low energy states and high energy states. The mean energy of state B, EB is taken to be greater than or equal to the mean energy of state A, EA. Denote the frequency difference between state B and state A by μ0=(EB−EA)/h, where h is Planck's constant.
When the quantities μ and μ0 are approximately equal, the quantum absorber can exhibit the phenomenon called Coherent-Population-Trapping (CPT), assuming that the value of νL falls in the necessary range so that the CPT-generating frequency component with frequency νL+½μ induces transitions between the state A and the states Ck, and the CPT-generating frequency component with frequency νL−½μ induces transitions between the state B and the states Ck. In this situation, the absorption (and fluorescence) of the CPT-generating components by the quantum absorber is smaller than it otherwise would be, and the transmission of the CPT-generating components through the quantum absorber is greater than it otherwise would be. When μ and μ0 are exactly equal, for fixed νL, the quantum absorber exhibits an absorption (and fluorescence) minimum, and a transmission maximum, of the CPT-generating components. One class of frequency standards utilizes the CPT phenomenon to adjust a frequency source such that its output frequency is equal to some function of μ0 by maintaining the frequency μ at the value that maximizes the transmission (or minimizes fluorescence) of the quantum absorber. If μ0 remains constant, then the frequency source can be used as a frequency standard having high accuracy, as long as a reliable method exists for determining μ0.
Therefore, reliably accurate frequency standards based on CPT must keep μ0 constant, and they must reliably determine the value of μ that maximizes the transmission through the absorber. To accomplish the first task, each source that causes μ0 to vary must be carefully controlled, or else means must be applied to the quantum absorber to reduce the sensitivity of μ0 to that source. For example, if the quantum absorber is 87Rb vapor in a cell with a buffer gas and a magnetic field, then some of the sources that cause μ0 to vary are fluctuations in the strength of the applied magnetic field, and the buffer gas pressure. Hence, reliable operation of the standard must ensure the constancy of the magnetic field and the buffer gas pressure.
For the purposes of the present discussion, it will be assumed that the standard measures the transmission through the quantum absorber. Similar arguments apply to standards that measure fluorescence, microwave emission, or some other parameter. In general, the transmitted power, T(νL, μ), will be a function of both νL and μ. Prior art methods determine the value of μ that maximizes the transmission by utilizing an algorithm that assumes that the transmission curve is a symmetric function of μ about μ0 for fixed νL when μ is near to μ0. If the transmission curve does not satisfy this symmetry condition, the determination of μ0 will be in error.
In quantum absorbers that exhibit the CPT phenomenon, T(νL, μ) is often not a symmetric function of μ about μ0 for fixed νL. Denote the Rabi frequency associated with the transition between state A and state Ck by ωAk and the Rabi frequency associated with the transition between state B and state Ck by ωBk. Then the transmission curve T(νL, μ), with νL held fixed, is a symmetric function of μ about μ0 only when, for each high energy state Ck, |ωAk|2=|ωBk|2. When this relation between ωAk and ωBk does not hold for each of the high energy states Ck, then T(νL, μ), for νL held fixed, will not normally be a symmetric function of μ about μ0, and an error will be made in the determination of the value of μ that maximizes the transmission through the quantum absorber.